# Comparing Polynomials and Complex Numbers by huanghengdong

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```									Comparing Polynomials and Complex Numbers               NAME

Similarities   Differences
Polynomials: (ax + by) + (cx + dy)
Complex: (a + bi) + (c + di)

SUBTRACTION
Polynomials: (ax + by) – (cx + dy)
Complex: (a + bi) – (c + di)

MULTIPLICATION
Polynomials: (ax + by) ● (cx + dy)
Complex: (a + bi)  (c + di)

BINOMIAL SQUARED
Polynomials: (ax + b)2
Complex: (a + bi)2

DIFFERENCE OF TWO SQUARES
Polynomial: (ax + b)(ax – b)
Complex: (a + bi)(a – bi)

DISTRIBUTIVE PROPERTY
Polynomial: d(ax + b)
Complex: d(a + bi)
Comparing Polynomials and Complex Numbers                                                     NAME                   KEY

Similarities                                       Differences
ADDITION                                  Combining like terms in both cases                In complex numbers, the real part of the
answer must be written first and then the
Polynomials: (ax + by) + (cx + dy)                                                            imaginary part.
Complex: (a + bi) + (c + di)

SUBTRACTION                               Combining like terms in both cases                Same as for addition
   Should rewrite second set of parentheses
Polynomials: (ax + by) – (cx + dy)         with the minus distributed
Complex: (a + bi) – (c + di)

MULTIPLICATION                            Will do FOIL method for each type                 FOIL always applies to complex but not to
polynomials (might be multiplying binomial
Polynomials: (ax + by) ● (cx + dy)                                                            by trinomial)
Complex: (a + bi)  (c + di)                                                                 In complex numbers an i will show up
2

BINOMIAL SQUARED                          Either FOIL or the 5-step shortcut applies        Binomial Squared will always result in a
to both situations                                 perfect square trinomial.
Polynomials: (ax + b)2                                                                       Complex Number squared will result in an
Complex: (a + bi)2                                                                            i showing up that must be adjusted out.
2

   Complex Number squared will still be a
binomial when finished.
DIFFERENCE OF TWO SQUARES                 Outer and inner products will cancel out          D2S for binomials still results in binomial
making FOIL unnecessary                            answer, but D2S for complex results in a
Polynomial: (ax + b)(ax – b)           
2        2
First – Second works for both                      single real number.
Complex: (a + bi)(a – bi)                                                                 
2
Complex D2S actually results in a + b if
2

shortcut based on i is remembered.
2

DISTRIBUTIVE PROPERTY                     Each term inside is multiplied by the term        If distributing a complex number, the order
of the final answer may change (if i
2
on the outside.
Polynomial: d(ax + b)                                                                         shows up it will).
Complex: d(a + bi)

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